Problem solving: pennies in bags

[Tulip]

Please could anyone help me on this question.


Sam divided 15 pennies among 4 small bags

He could then pay any sum of money from 1p to 15p, without opening any
bag.

How many pennies did Sam put in each bag?

[hermanmunster]

8,4,2, and 1

1=1
2=2
3=2+1
4=4
5=4+1
6=4+2
7=4+2+1
8=8
9=8+1
10=8+2
11=8+2+1
12=8+4
13=8+4+1
14=8+4+2
15=8+4+2+1

[moved]

Favourite problem I am sad!

[WP]

Another way of looking at this is as expressing numbers in binary (i.e. base 2), where a 1 means include the bag with 2^n pennies, and 0 means don't. For example:

11 (decimal) = 1011 (binary) = 8 + 2 + 1

You can write all the numbers from 0 to 15 with 4 binary digits.